一、年金终值系数指固定的间隔时间相等的期间(如以年为单位)分期支付(存入)1元金额,经过若干年后按复利计算的累计本利之和。
年金终值系数公式如下: ,这里F/A=(F/A,i,n)代表年金终值系数,i代表 利率,n代表年数。
二、 在Excel中我们可以使用FV财务函数计算年金终值系数,我们先来学习一下FV函数。FV 是一个财务函数,用于根据固定利率计算投资的未来值。 可以将 FV 与定期付款、固定付款或一次付清总额付款结合使用。 1.FV函数语法
FV(rate,nper,pmt,[pv],[type])
FV 函数有下列参数:
Rate 必需。 各期利率。
Nper 必需。 年金的付款总期数。
Pmt 必需。 各期所应支付的金额,在整个年金期间保持不变。 通常 pmt 包括本金和利息,但不包括其他费用或税款。 如果省略 pmt,则必须包括 pv 参数。
pv 可选。 现值,或一系列未来付款的当前值的累积和。 如果省略 pv,则假定其值为 0(零),并且必须包括 pmt 参数。
Type 可选。 数字 0 或 1,用以指定各期的付款时间是在期初还是期末。 如果省略 type,则假定其值为 0。
2. 假如我们计算3年期5%利率的年金终值系数,公式为FV(5%,3,-1, ,0),这里-1表示收到的金额,如下图所示。
图1.Excel函数FV计算年金终值系数。
附年金终值系数表
利率 |
1% |
2% |
3% |
4% |
5% |
6% |
7% |
8% |
9% |
10% |
期数 |
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|
|
|
|
|
|
|
|
|
1 |
1.0000 |
1.0000 |
1.0000 |
1.0000 |
1.0000 |
1.0000 |
1.0000 |
1.0000 |
1.0000 |
1.0000 |
2 |
2.0100 |
2.0200 |
2.0300 |
2.0400 |
2.0500 |
2.0600 |
2.0700 |
2.0800 |
2.0900 |
2.1000 |
3 |
3.0301 |
3.0604 |
3.0909 |
3.1216 |
3.1525 |
3.1836 |
3.2149 |
3.2464 |
3.2781 |
3.3100 |
4 |
4.0604 |
4.1216 |
4.1836 |
4.2465 |
4.3101 |
4.3746 |
4.4399 |
4.5061 |
4.5731 |
4.6410 |
5 |
5.1010 |
5.2040 |
5.3091 |
5.4163 |
5.5256 |
5.6371 |
5.7507 |
5.8666 |
5.9847 |
6.1051 |
6 |
6.1520 |
6.3081 |
6.4684 |
6.6330 |
6.8019 |
6.9753 |
7.1533 |
7.3359 |
7.5233 |
7.7156 |
7 |
7.2135 |
7.4343 |
7.6625 |
7.8983 |
8.1420 |
8.3938 |
8.6540 |
8.9228 |
9.2004 |
9.4872 |
8 |
8.2857 |
8.5830 |
8.8923 |
9.2142 |
9.5491 |
9.8975 |
10.2598 |
10.6366 |
11.0285 |
11.4359 |
9 |
9.3685 |
9.7546 |
10.1591 |
10.5828 |
11.0266 |
11.4913 |
11.9780 |
12.4876 |
13.0210 |
13.5795 |
10 |
10.4622 |
10.9497 |
11.4639 |
12.0061 |
12.5779 |
13.1808 |
13.8164 |
14.4866 |
15.1929 |
15.9374 |
11 |
11.5668 |
12.1687 |
12.8078 |
13.4864 |
14.2068 |
14.9716 |
15.7836 |
16.6455 |
17.5603 |
18.5312 |
12 |
12.6825 |
13.4121 |
14.1920 |
15.0258 |
15.9171 |
16.8699 |
17.8885 |
18.9771 |
20.1407 |
21.3843 |
13 |
13.8093 |
14.6803 |
15.6178 |
16.6268 |
17.7130 |
18.8821 |
20.1406 |
21.4953 |
22.9534 |
24.5227 |
14 |
14.9474 |
15.9739 |
17.0863 |
18.2919 |
19.5986 |
21.0151 |
22.5505 |
24.2149 |
26.0192 |
27.9750 |
15 |
16.0969 |
17.2934 |
18.5989 |
20.0236 |
21.5786 |
23.2760 |
25.1290 |
27.1521 |
29.3609 |
31.7725 |
16 |
17.2579 |
18.6393 |
20.1569 |
21.8245 |
23.6575 |
25.6725 |
27.8881 |
30.3243 |
33.0034 |
35.9497 |
17 |
18.4304 |
20.0121 |
21.7616 |
23.6975 |
25.8404 |
28.2129 |
30.8402 |
33.7502 |
36.9737 |
40.5447 |
18 |
19.6147 |
21.4123 |
23.4144 |
25.6454 |
28.1324 |
30.9057 |
33.9990 |
37.4502 |
41.3013 |
45.5992 |
19 |
20.8109 |
22.8406 |
25.1169 |
27.6712 |
30.5390 |
33.7600 |
37.3790 |
41.4463 |
46.0185 |
51.1591 |
20 |
22.0190 |
24.2974 |
26.8704 |
29.7781 |
33.0660 |
36.7856 |
40.9955 |
45.7620 |
51.1601 |
57.2750 |
21 |
23.2392 |
25.7833 |
28.6765 |
31.9692 |
35.7193 |
39.9927 |
44.8652 |
50.4229 |
56.7645 |
64.0025 |
22 |
24.4716 |
27.2990 |
30.5368 |
34.2480 |
38.5052 |
43.3923 |
49.0057 |
55.4568 |
62.8733 |
71.4027 |
23 |
25.7163 |
28.8450 |
32.4529 |
36.6179 |
41.4305 |
46.9958 |
53.4361 |
60.8933 |
69.5319 |
79.5430 |
24 |
26.9735 |
30.4219 |
34.4265 |
39.0826 |
44.5020 |
50.8156 |
58.1767 |
66.7648 |
76.7898 |
88.4973 |
25 |
28.2432 |
32.0303 |
36.4593 |
41.6459 |
47.7271 |
54.8645 |
63.2490 |
73.1059 |
84.7009 |
98.3471 |
26 |
29.5256 |
33.6709 |
38.5530 |
44.3117 |
51.1135 |
59.1564 |
68.6765 |
79.9544 |
93.3240 |
109.1818 |
27 |
30.8209 |
35.3443 |
40.7096 |
47.0842 |
54.6691 |
63.7058 |
74.4838 |
87.3508 |
102.7231 |
121.0999 |
28 |
32.1291 |
37.0512 |
42.9309 |
49.9676 |
58.4026 |
68.5281 |
80.6977 |
95.3388 |
112.9682 |
134.2099 |
29 |
33.4504 |
38.7922 |
45.2189 |
52.9663 |
62.3227 |
73.6398 |
87.3465 |
103.9659 |
124.1354 |
148.6309 |
30 |
34.7849 |
40.5681 |
47.5754 |
56.0849 |
66.4388 |
79.0582 |
94.4608 |
113.2832 |
136.3075 |
164.4940 |
31 |
36.1327 |
42.3794 |
50.0027 |
59.3283 |
70.7608 |
84.8017 |
102.0730 |
123.3459 |
149.5752 |
181.9434 |
32 |
37.4941 |
44.2270 |
52.5028 |
62.7015 |
75.2988 |
90.8898 |
110.2182 |
134.2135 |
164.0370 |
201.1378 |
33 |
38.8690 |
46.1116 |
55.0778 |
66.2095 |
80.0638 |
97.3432 |
118.9334 |
145.9506 |
179.8003 |
222.2515 |
34 |
40.2577 |
48.0338 |
57.7302 |
69.8579 |
85.0670 |
104.1838 |
128.2588 |
158.6267 |
196.9823 |
245.4767 |
35 |
41.6603 |
49.9945 |
60.4621 |
73.6522 |
90.3203 |
111.4348 |
138.2369 |
172.3168 |
215.7108 |
271.0244 |
36 |
43.0769 |
51.9944 |
63.2759 |
77.5983 |
95.8363 |
119.1209 |
148.9135 |
187.1021 |
236.1247 |
299.1268 |
37 |
44.5076 |
54.0343 |
66.1742 |
81.7022 |
101.6281 |
127.2681 |
160.3374 |
203.0703 |
258.3759 |
330.0395 |
38 |
45.9527 |
56.1149 |
69.1594 |
85.9703 |
107.7095 |
135.9042 |
172.5610 |
220.3159 |
282.6298 |
364.0434 |
39 |
47.4123 |
58.2372 |
72.2342 |
90.4091 |
114.0950 |
145.0585 |
185.6403 |
238.9412 |
309.0665 |
401.4478 |
40 |
48.8864 |
60.4020 |
75.4013 |
95.0255 |
120.7998 |
154.7620 |
199.6351 |
259.0565 |
337.8824 |
442.5926 |
41 |
50.3752 |
62.6100 |
78.6633 |
99.8265 |
127.8398 |
165.0477 |
214.6096 |
280.7810 |
369.2919 |
487.8518 |
42 |
51.8790 |
64.8622 |
82.0232 |
104.8196 |
135.2318 |
175.9505 |
230.6322 |
304.2435 |
403.5281 |
537.6370 |
43 |
53.3978 |
67.1595 |
85.4839 |
110.0124 |
142.9933 |
187.5076 |
247.7765 |
329.5830 |
440.8457 |
592.4007 |
44 |
54.9318 |
69.5027 |
89.0484 |
115.4129 |
151.1430 |
199.7580 |
266.1209 |
356.9496 |
481.5218 |
652.6408 |
45 |
56.4811 |
71.8927 |
92.7199 |
121.0294 |
159.7002 |
212.7435 |
285.7493 |
386.5056 |
525.8587 |
718.9048 |
46 |
58.0459 |
74.3306 |
96.5015 |
126.8706 |
168.6852 |
226.5081 |
306.7518 |
418.4261 |
574.1860 |
791.7953 |
47 |
59.6263 |
76.8172 |
100.3965 |
132.9454 |
178.1194 |
241.0986 |
329.2244 |
452.9002 |
626.8628 |
871.9749 |
48 |
61.2226 |
79.3535 |
104.4084 |
139.2632 |
188.0254 |
256.5645 |
353.2701 |
490.1322 |
684.2804 |
960.1723 |
49 |
62.8348 |
81.9406 |
108.5406 |
145.8337 |
198.4267 |
272.9584 |
378.9990 |
530.3427 |
746.8656 |
1057.1896 |
50 |
64.4632 |
84.5794 |
112.7969 |
152.6671 |
209.3480 |
290.3359 |
406.5289 |
573.7702 |
815.0836 |
1163.9085 |
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